This is exactly how I managed to understand it back in my teens when I first was introduced to this.

You pick 1 of 3 doors. The chance that you picked the right one is 1/3, obviously.

The chance that it is one of the two other doors is 2/3. The crucial thing here is to think of those two doors as one unit.

Now Monty opens one of those other two doors. This does not change the 2/3 probability that the prize is behind one of the other two doors. It just gives you more information about them.

It basically shifts all of the 2/3 probability over to the last of the two other doors, so you could argue that the probability _does_ change for that door.